Implementing Newton’s method in python for root-finding in differentiable functions
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Authors
Raridan, Christopher
Roberson, Spencer
Roberts, Alexa
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Article
Language
en
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Abstract
Newton’s Method is an iterative technique that uses tangent lines to approximate roots of real-valued, differentiable functions. This paper explores the method’s application as a strategy for finding real roots when exact solutions are difficult to obtain algebraically. The method was implemented in Python and applied to a variety of functions, including a low-degree polynomial, a high-degree polynomial, a trigonometric function, and an exponential function. The approximation process starts by evaluating each function at integer values between –10 and 10. If a function evaluated to zero at any of these values, a root is found immediately. Otherwise, the Intermediate Value Theorem is used to locate intervals where the function changed sign, indicating the presence of a root. One of these values is then selected as an initial approximation for Newton’s Method. Using the iterative formula, each initial guess is refined to converge toward the actual root. The method produced accurate approximations across all function types when an initial guess was sufficiently close to the true root, demonstrating the efficiency of Newton’s Method in iterative root-finding.
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Clayton State University